Question

A thrift store allows customers to buy or donate clothing items. The store ends off the first day of the month with 58
pieces of clothing. After each subsequent day, the store has a net 28
additional pieces of clothing.

Model the situation above with an explicit formula for the sequence. Let
be the number of pieces of clothing the store has after the
th day of the month.

Answer 1

To model the situation described, we want to establish an explicit formula for the number of pieces of clothing, \( C(n) \), that the thrift store has after \( n \) days of the month.

We know the following:
- On the first day of the month (when \( n = 0 \)), the store has 58 pieces of clothing.
- After each subsequent day, the store gains a net of 28 pieces of clothing.

This means that for each day after the first, the number of pieces of clothing increases by 28. Therefore, we can define \( C(n) \) as follows:

1. On day \( n = 0 \):
\[
C(0) = 58
\]

2. For each subsequent day \( n \) (where \( n \geq 1 \)):
\[
C(n)= 58 + 28n
\]

Putting this together, the explicit formula for the number of pieces of clothing in the store after \( n \) days is:
\[
C(n) = 58 + 28n
\]

This formula gives the total number of pieces of clothing after any given number of days \( n \).